Cryptology ePrint Archive: Report 2013/793

A fast integer-based batch full-homomorphic encryption scheme over finite field

Long Zhang and Qiuling Yue

Abstract: In view of the problems that the plaintext space is too small in the existing schemes. In this paper, a new improved scheme is presented by improving the DGHV scheme. The plaintext space of the improved scheme is extended from finite prime field $F_{2}$ in the original scheme to finite prime field $F_{p}$. Combine and apply the method of encryption in the batch encryption scheme was proposed in 2013, and the plaintext space is further extended to finite fields $F_{q}$.
The new improved scheme encrypts the message by applying the modular mathematical operation
and the Chinese remainder theorem, and the security of the scheme is based on the the difficulty of approximate greatest common divisor problem and the spare subset sum problem. The improved scheme we got has the advantages of encrypt fast, and the size of ciphertext is small. So compared with the original scheme, it is better for practical application.